The generalized singular value decomposition (GSVD) often is used to solve Tikhonov regularization problems with a regularization matrix without exploitable structure. This paper describes how the standard methods for the computation of the GSVD of a matrix pair can be simplified in the context of Tikhonov regularization. Also, other regularization methods, including truncated GSVD, are conside...

Large linear discrete ill-posed problems with contaminated data are often solved with the aid of Tikhonov regularization. Commonly used regularization matrices are finite difference approximations of a suitable derivative and are rectangular. This paper discusses the design of square regularization matrices that can be used in iterative methods based on the Arnoldi process for large-scale Tikho...

This paper proposes a novel regularization approach for Extreme Learning Machines. Regularization is performed using a priori spacial information expressed by an affinity matrix. We show that the use of this type of a priori information is similar to perform Tikhonov regularization. Furthermore, if a parameter free affinity matrix is used, like the cosine similarity matrix, regularization is pe...

In this paper we establish a regularization method for Radon measures. Motivated from sparse L regularization we introduce a new regularization functional for the Radon norm, whose properties are then analyzed. We, furthermore, show well-posedness of Radon measure based sparsity regularization. Finally we present numerical examples along with the underlying algorithmic and implementation detail...

The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with dimensional regularization to obtain a consistent renormalized 4-dimensional Yang-Mills theory at the one-loop level. This shows that hybrid regularization methods ...

Regularization is an well-known technique for obtaining stable solution of ill-posed inverse problems. In this paper we establish a key relationship among the regularization methods with an edge-preserving noise filtering method which leads to an efficient adaptive regularization methods. We show experimentally the efficiency and superiority of the proposed regularization methods for some inver...

The generalization ability of a neural network can sometimes be improved dramatically by regularization. To analyze the improvement one needs more refined results than the asymptotic distribution of the weight vector. Here we study the simple case of one-dimensional linear regression under quadratic regularization, i.e., ridge regression. We study the random design, misspecified case, where we ...

We derive the correspondence between regularization operators used in Regularization Networks and Hilbert Schmidt Kernels appearing in Support VectorMachines. More specifically, we prove that the Green’s Functions associated with regularization operators are suitable Support Vector Kernels with equivalent regularization properties. As a by–product we show that a large number of Radial Basis Fun...

In this paper, we proposed a new model with nuclear-norm and L1-norm regularization for image reconstruction in aerospace remote sensing. The curvelet based L1-norm regularization promotes sparse reconstruction, while the low-rank based nuclear-norm regularization leads to a principle component solution. Split Bregman method is used to solve this problem. Numerical experiments show the proposed...

In this paper, we study a Tikhonov-type regularization for restricted Boltzmann machines (RBM). We present two alternative formulations of the Tikhonov-type regularization which encourage an RBM to learn a smoother probability distribution. Both formulations turn out to be combinations of the widely used weight-decay and sparsity regularization. We empirically evaluate the effect of the propose...